# Introduction to work and energy

## Video udskrift

Welcome back. I'm now going to introduce you to the concepts of work and energy. And these are two words that are-- I'm sure you use in your everyday life already and you have some notion of what they mean. But maybe just not in the physics context, although they're not completely unrelated. So work, you know what work is. Work is when you do something. You go to work, you make a living. In physics, work is-- and I'm going to use a lot of words and they actually end up being kind of circular in their definitions. But I think when we start doing the math, you'll start to get at least a slightly more intuitive notion of what they all are. So work is energy transferred by a force. So I'll write that down, energy transferred-- and I got this from Wikipedia because I wanted a good, I guess, relatively intuitive definition. Energy transferred by a force. And that makes reasonable sense to me. But then you're wondering, well, I know what a force is, you know, force is mass times acceleration. But what is energy? And then I looked up energy on Wikipedia and I found this, well, entertaining. But it also I think tells you something that these are just concepts that we use to, I guess, work with what we perceive as motion and force and work and all of these types of things. But they really aren't independent notions. They're related. So Wikipedia defines energy as the ability to do work. So they kind of use each other to define each other. Ability to do work. Which is frankly, as good of a definition as I could find. And so, with just the words, these kind of don't give you much information. So what I'm going to do is move onto the equations, and this'll give you a more quantitative feel of what these words mean. So the definition of work in mechanics, work is equal to force times distance. So let's say that I have a block and-- let me do it in a different color just because this yellow might be getting tedious. And I apply a force of-- let's say I apply a force of 10 Newtons. And I move that block by applying a force of 10 Newtons. I move that block, let's say I move it-- I don't know-- 7 meters. So the work that I applied to that block, or the energy that I've transferred to that block, the work is equal to the force, which is 10 Newtons, times the distance, times 7 meters. And that would equal 70-- 10 times 7-- Newton meters. So Newton meters is one, I guess, way of describing work. And this is also defined as one joule. And I'll do another presentation on all of the things that soon. Joule did. But joule is the unit of work and it's also the unit of energy. And they're kind of transferrable. Because if you look at the definitions that Wikipedia gave us, work is energy transferred by a force and energy is the ability to work. So I'll leave this relatively circular definition alone now. But we'll use this definition, which I think helps us a little bit more to understand the types of work we can do. And then, what kind of energy we actually are transferring to an object when we do that type of work. So let me do some examples. Let's say I have a block. I have a block of mass m. I have a block of mass m and it starts at rest. And then I apply force. Let's say I apply a force, F, for a distance of, I think, you can guess what the distance I'm going to apply it is, for a distance of d. So I'm pushing on this block with a force of F for a distance of d. And what I want to figure out is-- well, we know what the work is. I mean, by definition, work is equal to this force times this distance that I'm applying the block-- that I'm pushing the block. But what is the velocity going to be of this block over here? Right? It's going to be something somewhat faster. Because force isn't-- and I'm assuming that this is frictionless on here. So force isn't just moving the block with a constant velocity, force is equal to mass times acceleration. So I'm actually going to be accelerating the block. So even though it's stationary here, by the time we get to this point over here, that block is going to have some velocity. We don't know what it is because we're using all variables, we're not using numbers. But let's figure out what it is in terms of v. So if you remember your kinematics equations, and if you don't, you might want to go back. Or if you've never seen the videos, there's a whole set of videos on projectile motion and kinematics. But we figured out that when we're accelerating an object over a distance, that the final velocity-- let me change colors just for variety-- the final velocity squared is equal to the initial velocity squared plus 2 times the acceleration times the distance. And we proved this back then, so I won't redo it now. But in this situation, what's the initial velocity? Well the initial velocity was 0. Right? So the equation becomes vf squared is equal to 2 times the acceleration times the distance. And then, we could rewrite the acceleration in terms of, what? The force and the mass, right? So what is the acceleration? Well F equals ma. Or, acceleration is equal to force divided by you mass. So we get vf squared is equal to 2 times the force divided by the mass times the distance. And then we could take the square root of both sides if we want, and we get the final velocity of this block, at this point, is going to be equal to the square root of 2 times force times distance divided by mass. And so that's how we could figure it out. And there's something interesting going on here. There's something interesting in what we did just now. Do you see something that looks a little bit like work? Well sure. You have this force times distance expression right here. Force times distance right here. So let's write another equation. If we know the given amount of velocity something has, if we can figure out how much work needed to be put into the system to get to that velocity. Well we can just replace force times distance with work. Right? Because work is equal to force times distance. So let's go straight from this equation because we don't have to re-square it. So we get vf squared is equal to 2 times force times distance. That's work. Took that definition right here. 2 times work divided by the mass. Let's multiply both sides of this equation times the mass. So you get mass times the velocity. And we don't have to write-- I'm going to get rid of this f because we know that we started at rest and that the velocity is going to be-- let's just call it v. So m times V squared is equal to 2 times the work. Divide both sides by 2. Or that the work is equal to mv squared over 2. Just divided both sides by 2. And of course, the unit here is joules. So this is interesting. Now if I know the velocity of an object, I can figure out, using this formula, which hopefully wasn't too complicated to derive. I can figure out how much work was imputed into that object to get it to that velocity. And this, by definition, is called kinetic energy. This is kinetic energy. And once again, the definition that Wikipedia gives us is the energy due to motion, or the work needed to accelerate from an object from being stationary to its current velocity. And I'm actually almost out of time, but what I will do is I will leave you with this formula, that kinetic energy is mass times velocity squared divided by 2, or 1/2 mv squared. It's a very common formula. And I'll leave you with that and that is one form of energy. And I'll leave you with that idea. And in the next video, I will show you another form of energy. And then, I will introduce you to the law of conservation of energy. And that's where things become useful, because you can see how one form of energy can be converted to another to figure out what happens to an object. I'll see